Vector Control Drive of Permanent Magnet Motor without a Shaft Encoder

Transcription

1 Vector Control Drive of Permanent Magnet Motor without a Shaft Encoder Eng. Mona F. Moussa* Prof. Yasser Gaber Prof. Magdy El Attar (Arab Academy for science and technology) *mona.moussa@yahoo.com Alexandria University Abstract Permanent Magnet Synchronous Motors (PMSMs) are receiving increased attention for drive applications because of their high toque to inertia ratio, superior power density, and high efficiency. To control PMSM, position and speed sensors are indispensable because the current should be controlled depending on the rotor position. However, these sensors are undesirable from standpoints of size, cost, maintenance, and reliability. There are different ways of approaching this problem, depending on the flux distribution. This paper presents a novel vector control for a permanent motor drive without use of a shaft sensor. The vector control drive provides a wide range of speeds, high torque capability and high efficiency. Two line-to-line voltages and two stator currents are sensed to produce the stator flux linkage space vector. The angle of this vector is then used to produce the appropriate stator current command signals which can be controlled to maintain zero d-axis current which is the condition of vector control, over a wide range of torque and speed. A speed signals is derived from the rate of change of angle of the flux linkage. Simulation is carried out in order to evaluate the behavior of the proposed method for different operating situations. The simulation results demonstrate that a good steady-state and transient performances for the proposed sensorless scheme are obtained. Keywords Permanent magnet synchronous motor (PMSM), vector control, sensorless control. List of symbols R a L d, L q v d, v q i d, i q d, q, f P i, P o,,,, i a, i b v ab, v bc θ r, θ S θl Stator resistance. d-and q-axis inductances. d-and q-axis components of stator voltages. d-and q-axis components of stator currents. d-and q-axis flux linkage. Electrical rotor angular speed and estimated speed. Constant flux linkage due to rotor permanent magnet. Input power, and output power. Space vector of stator phase flux linkage, e.m.f, and voltage. Space vector of stator line-to-line stator flux linkage, e.m.f, and voltage. Space vector of line stator current. Stator phase currents. Stator phase voltages. Rotor position, and stator position. Space angle of the flux-linkage. I. INTRODUCTION Improvement of Permanent Magnet (PM) materials is widening the application of PMSMs. Recently, with the advent of high performance (PM) with high coactivity and high residual flux, it has been possible for the PM motors to be superior to general-purpose induction motors in power dentistry, torque-to-inertia ratio, and efficiency. Therefore, the PM motors are of more interest in many industrial applications as substitutes for induction motors. Also, the vector control of PM motors is much simpler than of induction motors because there is no-need to consider the slip frequency as in induction motor drive []. However, conventional vector control of PM motor drives requires a motor position sensor to correctly orient the current vector orthogonally to the flux because the rotor flux is obtained from permanent magnets. In such a way, it is possible to directly control the toque by acting simply on the amplitude of the stator current. Thus, we can achieve a high degree of toque control over a wide speed range including the standstill can be achieved []. These position sensors or rotational transducers not only increase cost, maintenance, and complexity of the drive, but also impair robustness and reliability of the drive system. Therefore, many researchers have been studying the sensorless drive of the PM motor in view of the robustness, reliability, cost, and so on []-[8]. These sensorless techniques can be classified into three categories such as; ) Position sensing using back e.m.f of the motor. This method can be based on Kalman filtering [], [] or state observer []-[8]. ) Position sensing using inductance variation [9]-[]. ) Position sensing using flux-linkage variation, which may be based on the measurement of voltages and currents []-[7], or on the hypothetical rotor position [8]. In this paper, the proposed sensorless scheme is based on sensing the position via flux-linkage variation. By using motor voltage and currents, synthesis of the flux linkage position signal through which the phase angle of the stator current is controlled. The flux linkage space phasor can be obtained by interesting the back e.m.f which is calculated from measured voltages and currents. This technique represents a simple control system for a PM motor drive with sinusoidal phase current supply, and provides a wide speed range without a shaft encoder. In [], the method of position sensing had satisfied the condition of unity power factor operation for PMSM. However, this control strategy in not the optimal in terms of torque production, since the efficiency will not be maximum as the d-axis stator current will not equal zero. It can be shown that vector control drive corresponds to maximum efficiency maximum and maximum torque per ampere as follows: The d-q- stator voltage equations of the PMSM in the steady-state operation are expressed as [9]: () () The input power P i and the developed power P o are given by:

2 () () And the efficiency () The value of current i d corresponding to maximum efficiency η is obtained from the equation: η () This tends to: (7) For PM motors which have identical rotor structure, the inductance of d-axis equals to that of the q-axis. Substituting L d = L q into () yields; maximum efficiency takes place when i d equals zero. Therefore, in vector control of PMSM, a high dynamic performances without using an excessive current can be achieved if the magnetizing competent i d of the stator current is maintained at zero, while the torque is controlled using the quadrature component i q to get optimal type of control and obtain minimum input power and hence, maximum efficiency []. That is why, in this paper a novel sensorless drive is based on the vector control scheme of PMSM. II. PROPOSED SENSORLESS VECTOR CONTROL DRIVE SYSTEM Recently, many researches are carried out to sensorless control of PMSM vector control drive based on the idea of calculating the rotor position through an estimated angle where the stator voltages and currents signals are used to estimate the instantaneous flux linkage position signal through which the phase angle of the stator current can be controlled to maintain the d-axis current equal to zero over a wide range of torque and speed [7]. A space vector diagram for a PM motor is shown in Fig., in which is the line-to neutral e.m.f space vector, and is Fig. Space vector diagram for sensorless vector controlled PMSM drive. the phase current vector. The phase flux linkage space vector is obtained by integration of. Since the motor normally has no neutral connections, only line voltages are available. The line- to-line e.m.f is denoted as, leading by in angular space. The line-to-line flux linkage corresponding to is. The e.m.f space vector can be determined from measurements of stator line-to-line voltage v ab and v bc and stator phase current i a and i b as follows: (7) This equation can be expressed in line values as: (8) The line-to-line stator voltage vector is given by: (9) And the line current vector is: () Substitution of (9) and () into (8) yields () Where, () () () The flux linkage space vector is derived from the e.m.f as: () The real and imaginary components of flux linkage can now be related to the measured quantities by: () (7) The space angle of the flux linkage is: tan (8) Since the line-to-line e.m.f is leading the line-to-neutral e.m.f by in angular space, and since the line-to-neutral e.m.f is leading the stator phase flux linkage space vector by 9, and also is leading by 9, then, the stator phase e.m.f should lead the line space vector by as should as shown in Fig.. (9) () For vector control, in order to decouple the two components of stator current; namely the flux producing current (i d ) and the torque producing current (i q ), i d should be zero. Therefore, an independent control of torque and flux is achieved similar to a separately-excited DC motor. Hence, () From the above space vector diagram, it is clear that the rotor angle θ r is lagging the stator angle θ S by the angle α v, which is the angle between the d-q frame (rotor frame) and the estimated or e.m.f frame (-β frame of and ). α () Thus, substituting () into (), the stator current command vector should have the form:

3 α () The three phase current commands should then have the instantaneous values: cos cos () Such that, the angle α v between the line-to-neutral e.m.f space vector and the stator current space vector, can be calculated as follows: α tan () Where, () And, for vector control since, (7) Substituting () and (7) into () gives: α tan (8) III. IMPLEMENTATION Fig. shows a block diagram of the drive system. The system basically has two control loops. In the inner current loop, the two stator terminal voltages and currents are sensed, combined, and integrated first in order to obtain the flux space angle θ o φl (see () to (7)). The angle θ S of the stator phase e.m.f space vector is obtained by a º shift ahead to θ φl (see ()). The angle α v between the vector phase e.m.f space vector and the stator current space vector is calculated (see (8)). Then, the current command angle θ r is obtained by subtracting the angle θ s from the calculated angle α v, (angle between rotor frame and e.m.f frame). Thus, the two cosine functions cos(θ S -α v ) and cos(θ S -α v - o ) of the two command currents can be generated. Also, the magnitude i * S of the two command currents can be obtained from the outer speed loop, such that, the error signal between the command speed signal * and the estimated speed f is implemented to a proportional and integral controller, whose, output is the command q-axis component of current i * q which equals to the command stator current i * s (see ()). Now, the three command currents can be generated (see ()). A signal proportional to the motor speed is calculated by the differentiation of the angle θ φl (9) Due to the accuracy and flexibility of the digital signal processor DSP, the above calculations including trigonometric functions, phase shift, differentiation, beside the digital integration can be easily performed. Because θ φl is obtained from an integration of the stator voltages and currents with their high frequency switched waveform resulted from PWM, the differentiation will amplify the high frequency noise in θ φl. To eliminate this noise, a low pass filter is required. This is also done in digital form within the DSP. In implementing this vector control system, the drift of the integrators limits the accuracy of both flux position and speed calculation. That is why; a drift compensation technique like that proposed in [] may be used to ensure that the average flux linkage with each phase will be zero when the machine operates at steady-state speed and torque. Consequently the calculation errors due to various drift-sources will be effectively reduced. It is clear from Fig. that, the locus of the flux vector will be a circle in the steady state and will depart only slightly from a circle during a transient since most of the flux linkage arises from the motor magnets. The maximum and minimum real and imaginary components of the drift can be determined each cycle to give: Fig. Block diagram of the sensorless vector controlled PMSM drive system. Fig. Locus of the flux linkage vector with drift.

4 () Then, the calculated angle will become: tan () Therefore, the two components of flux linkage, the real component φ LR and the imagining component φ LI will appear without any drift or offset. Near standstill, the e.m.f is too small to be sensed accurately [], []. Thus, an open loop control is necessary to accelerate the motor from standstill to the speed at which the flux linkage angle can be determined. A ramp speed command starting profile; like that described in []; can be applied to provide a smooth start up transient response for the proposed sensorless control scheme, and overcome the starting problem. It should be noted that, there is a low-frequency limit of control for this vector control sensorless drive, beyond which the stator terminal voltage is dominated by the resistance drop and also the e.m.f residue combined with the inverter noise is inadequate to determine the flux linkage angle. However, several techniques have been proposed to solve this low speed limitation problem [], []. Another limitation of this scheme is its dependence on the parameter sensitivity of the motor such as; the stator resistance by the temperature changes. To solve this disadvantage, parameter identification is proposed in []. IV. SIMULATION RESULTS Simulation of the system has been carried out using Matlab-Simulink, in order to evaluate the behavior of the proposed sensorless vector control drive system. Fig. shows the transient response of the system due to a step change of the speed command signal from the full load speed 7 rad/sec to rad/sec at time t =. sec, and a step from rad/sec at time t = sec to rad/sec, at full load torque (Nm). Fig. shows the low frequency performance of the sensorless control system with a step change of the load torque from to Nm at time sec. The simulation results demonstrate that the system can operate adequately at speed = 7 rad/sec (i.e. % of the full load speed). The relative error between the actual and estimated speed is equal to zero in steady-state. And the control performance is satisfactory (rapid transient response, small steady state error). Moreover, the estimated position and speed follow exactly the rotor speed and position over a wide range of speed and torque. Therefore, the proposed controlled algorithm has good performance for replacing a shaft sensor over a wide speed range. To overcome the starting problem, an open-loop control is necessary to accelerate the motor from standstill to the speed at which the flux linkage angle can be reliably determined. Moreover, speed oscillation during the starting process may be minimized by establishing the proper initial rotor angle []. One method is to apply a fixed current vector to the motor at standstill and allow its angular oscillation to decay to a predetermined position []. Fig. shows the starting performance of the proposed sensorless drive system. Reference, motor and estimated speed (rad/sec) d- axis stator current id (Amp) Rotor position (rad) Estimated position t Step change of speed (a) (c) (e) (f) Fig. Simulation results of the proposed sensorless vector controlled drive system. (a) (c) t At step change of speed t Reference speed Motor speed Estimated speed At rated speed = 7 rad/sec & load torque = Nm & step change of load torque from to Nm Reference, motor and estimated speed (rad/sec) Load and electromagnetic torque (Nm) Real & imaginary components of line flux linkage t Reference speed Motor speed Estimated speed Load torque Electromagnetic torque Real component of flux linkage Imaginary component of flux linkage (e) (f) Fig. Low frequency performance of the sensorless control system. Angle between rotor & emf frame alphav (rad) Load and electromagnetic torque (Nm) q axis current iq (Amp) Phase voltage va (volt) Estimated position (rad) Rotor position (rad) q-axis stator current (Amp) Step change of speed t (b) (d) (b) (d) Load torque Electromagnetic torque t At step change of speed t t At step change of speed t t

5 Reference, motor and estimated speed (rad/sec) Reference stator current (Amp) Starting performance at rad/sec Reference speed Motor speed Estimated speed (a) Starting performance at rad/sec -... (c) (d) Fig. Starting performance of the proposed sensorless drive system. An open loop control is applied to accelerate the speed from standstill to the speed at which the flux linkage angle θ ΦL can be determined. From the above figures, it is clear that the initial acceleration is limited by the current limit, and the speed response has a small overshoot. Often the problem of a controlled startup is avoided all together the by using openloop start-up techniques, which provide little control of the torque with unnecessarily high currents. V. DISCUSSION The problem of controlling torque, flux, and speed without mechanical sensors in a PMSM drive has been analyzed []. Most of these sensorless techniques are based on two basic ideas in the implementation irrelevant on the theory of operation which are: - Measuring the rotor position θ r itself like [8] by using an estimated frame parallel to the original (rotor or d-q frame). This method is usually applied for the conventional decoupled vector control, where i d =. In most of these cases, in the current inner loop, there will be a comparison between the actual d and q axis stator currents i d, i q and with the command reference d and q-axis i d * and i q *. The limitation of this method is its sensitivity to all motor parameters. - Measuring the stator angle θ S itself like [] by calculating the flux linkage from the currents and voltages. This method has been implemented for unity power factor control drive system, where, in the inner current loop, there will be comparison between the actual phase currents i a, i b, i c with the generated command currents i a *, i b *, i c *. The advantage of this method is its dependence on the stator resistance only. But, it has been proven that the decoupled vector control is better than the unity power factor control since it gives maximum efficiency and maximum torque per ampere current ratio []. For this reason, the method presented in this paper will be based on the decoupled vector control by determining the Load torque (Nm) Estimated position (rad) Rotor position (rad) Starting performance at rad/sec (b) Starting performance at rad/sec flux linkage angle and the number of the motor parameters which are required will be reduced by one. VI. SYSTEM DESCRIPTION Table. -φ Sinusoidal back-emf PMSM Rating and Parameters R a.87ω L d = L q Φ f n rating T rating 8.mH.7 V/rad/s r.p.m Nm J.8* - Kg-m f Power V rated frequency.nm/rad/s. kw V Hz VII. CONCLUSION The problem of controlling torque, flux, and speed without mechanical sensors in a PMSM drive has been analyzed. Most of these sensorless techniques are based on two basic ideas as follows: - Measuring the rotor position θ r itself like [8] by using an estimated frame parallel to the original (rotor or d-q frame). This method is usually applied for the conventional decoupled vector control, where i d =. The limitation of this method is its sensitivity to all motor parameters. - Measuring the stator angle θ S itself like [] by calculating the flux linkage from the currents and voltages. This method has been implemented for unity power factor control drive system; the advantage of this method is its dependence on the stator resistance only. But, it has been proven that the decoupled vector control is better than the unity power factor control since it gives maximum efficiency and maximum torque per ampere current ratio. A novel sensorless vector control drive is presented which enables to control motor torque and flux using sufficient and suitable information from the stator voltages and currents to obtain the stator flux angle θ φl, which is differentiated to give the estimated speed signal ω f. Then, the command current angle θ r which is the difference between the stator angle θ S and load angle α v is calculated. This angle is used to enforce the d-axis component of current to be zero. Consequently, the * command stator current i S is will equal to the q-axis component of current i * q. Thus, the required decoupling for the two components of stator current is achieved. Hence, a high dynamic performance without using an excessive current can be achieved since the magnetizing component i d of the stator current is zero, while the torque is controlled using the quadrature component i q. The simulation results demonstrate that stator voltage and current signals from a PMSM can be successfully used in a simple vector control system to obtain the necessary position

6 and speed information for replacing a shaft encoder over a wide speed range. The system works particularly well with a PMSM. A relatively smooth start can be achieved with open loop using a ramp acceleration prior to applying the closed loop control speed. The system is considered to be adequate for the majority of drives that do not require full controlled torque operation down to zero speed. REFERENCES [] Paul P. Acarnley and John F. Wastson, Review of Position- Sensorless Operation of Brushless Permanent-Magnet Machines, IEEE Trans. Ind. Electron., vol., no., April. [] Bon- Ho Bae, IEEE, Seung-Kisal, Jeong-Hyeck Kwon, and Jiseob Beyon, Implementation of sensorless vector control for super-highspeed PMSM of Turbo -compressor, IEEE Ind. Appl., vol. 9, no., May/June. [] Manfred Schroedl, Sensorless control of permanent magnet synchronous motors, Taylor & Francis, Inc., Washington, DC, vol., pp. 7-8, 99. 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